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DOE OSTI2017

Multifield stochastic particle production: beyond a maximum entropy ansatz

In this work, we explore non-adiabatic particle production for N f coupled scalar fields in a time-dependent background with stochastically varying effective masses, cross-couplings and intervals between interactions. Under the assumption of weak scattering per interaction, we provide a framework for calculating the typical particle production rates after a large number of interactions. After setting up the framework, for analytic tractability, we consider interactions (effective masses and cross couplings) characterized by series of Dirac-delta functions in time with amplitudes and locations drawn from different distributions. Without assuming that the fields are statistically equivalent, we present closed form results (up to quadratures) for the asymptotic particle production rates for the N f =1 and N f =2 cases. We also present results for the general N f >2 case, but with more restrictive assumptions. We find agreement between our analytic results and direct numerical calculations of the total occupation number of the produced particles, with departures that can be explained in terms of violation of our assumptions. We elucidate the precise connection between the maximum entropy ansatz (MEA) used in Amin & Baumann (2015) and the underlying statistical distribution of the self and cross couplings. We provide and justify a simple to use (MEA-inspired) expression for the particle production rate, which agrees with our more detailed treatment when the parameters characterizing the effective mass and cross-couplings between fields are all comparable to each other. However, deviations are seen when some parameters differ significantly from others. We show that such deviations become negligible for a broad range of parameters when N f >> 1.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The stochastic spectator

We study the stochastic distribution of spectator fields predicted in different slow-roll inflation backgrounds. Spectator fields have a negligible energy density during inflation but may play an important dynamical role later, even giving rise to primordial density perturbations within our observational horizon today. During de-Sitter expansion there is an equilibrium solution for the spectator field which is often used to estimate the stochastic distribution during slow-roll inflation. However slow roll only requires that the Hubble rate varies slowly compared to the Hubble time, while the time taken for the stochastic distribution to evolve to the de-Sitter equilibrium solution can be much longer than a Hubble time. We study both chaotic (monomial) and plateau inflaton potentials, with quadratic, quartic and axionic spectator fields. We give an adiabaticity condition for the spectator field distribution to relax to the de-Sitter equilibrium, and find that the de-Sitter approximation is never a reliable estimate for the typical distribution at the end of inflation for a quadratic spectator during monomial inflation. The existence of an adiabatic regime at early times can erase the dependence on initial conditions of the final distribution of field values. In these cases, spectator fields acquire sub-Planckian expectation values. Otherwise spectator fields may acquire much larger field displacements than suggested by the de-Sitter equilibrium solution. We quantify the information about initial conditions that can be obtained from the final field distribution. Our results may have important consequences for the viability of spectator models for the origin of structure, such as the simplest curvaton models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Quantum diffusion during inflation and primordial black holes

We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-δ N formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. In the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than ∼ 1 e -fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The matrix product approximation for the dynamic cavity method

Stochastic dynamics of classical degrees of freedom, defined on vertices of locally tree-like graphs, can be studied in the framework of the dynamic cavity method which is exact for tree graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, and other technical, biological, and social networks. The central objects in the cavity method are edge messages—conditional probabilities of two vertex variable trajectories. In this paper, we discuss a rather pedagogical derivation for the dynamic cavity method, give a detailed account of the novel matrix product edge message (MPEM) algorithm for the solution of the dynamic cavity equation as introduced, and present optimizations and extensions. Matrix product approximations of the edge messages are constructed recursively in an iteration over time. Computation costs and precision can be tuned by controlling the matrix dimensions of the MPEM in truncations. Without truncations, the dynamics is exact. Data for Glauber–Ising dynamics shows a linear growth of computation costs in time. In contrast to Monte Carlo simulations, the approach has a much better error scaling. Hence, it gives for example access to low probability events and decaying observables like temporal correlations. Here, we discuss optimized truncation schemes and an extension that allows to capture models which have a continuum time limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Nonequilibrium formulation of varying-temperature bit erasure

Landauer's principle states that erasing a bit of information at fixed temperature T costs at least $k$ B $T$ ln 2 units of work. Here we investigate erasure at varying temperature, to which Landauer's result does not apply. Here we formulate bit erasure as a stochastic nonequilibrium process involving a compression of configuration space, with physical and logical states associated in a symmetric way. Erasure starts and ends at temperature T, but temperature can otherwise vary with time in an arbitrary way. Defined in this way, erasure is governed by a set of nonequilibrium fluctuation relations that show that varying-temperature erasure can done with less work than $k$ B $T$ ln 2. As a result, erasure and the complementary process of bit randomization can be combined to form a work-producing engine cycle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

STOCHASTIC STAR FORMATION AND A (NEARLY) UNIFORM STELLAR INITIAL MASS FUNCTION

Recent observations indicate a lower H{alpha} to FUV ratio in dwarf galaxies than in brighter systems, a trend that could be explained by a truncated and/or steeper initial mass function (IMF) in small galaxies. However, at low star formation rates (SFRs), the H{alpha} to FUV ratio can vary due to stochastic sampling even for a universal IMF, a hypothesis that has, prior to this work, received limited investigation. Using SLUG, a fully stochastic code for synthetic photometry in star clusters and galaxies, we compare the H{alpha} and FUV luminosity in a sample of {approx}450 nearby galaxies with models drawn from a universal Kroupa IMF and a modified IMF, the integrated galactic initial mass function (IGIMF). Once random sampling and time evolution are included, a Kroupa IMF convolved with the cluster mass function (CMF) reproduces the observed H{alpha} distribution at all FUV luminosities, while a truncated IMF as implemented in current IGIMF models underpredicts the H{alpha} luminosity by more than an order of magnitude at the lowest SFRs. We conclude that the observed luminosity is the result of the joint probability distribution function of the SFR, CMF, and a universal IMF, consistent with parts of the IGIMF theory, but that a truncation in the IMF in clusters is inconsistent with the observations. Future work will examine stochastic star formation and its time dependence in detail to study whether random sampling can explain other observations that suggest a varying IMF.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

'LEADING BLOB' MODEL IN A STOCHASTIC ACCELERATION SCENARIO: THE CASE OF THE 2009 FLARE OF Mkn 501

Evidence for very hard, intrinsic {gamma}-ray source spectra, as inferred after correction for absorption in the extragalactic background light (EBL), has interesting implications for the acceleration and radiation mechanisms acting in blazars. A key issue so far has been the dependence of the hardness of the {gamma}-ray spectrum on different existing EBL models. The recent Fermi observations of Mkn 501 now provide additional evidence for the presence of hard intrinsic {gamma}-ray spectra independent of EBL uncertainties. Relativistic Maxwellian-type electron energy distributions that are formed in stochastic acceleration scenarios offer a plausible interpretation for such hard source spectra. Here, we show that the combined emission from different components with Maxwellian-type distributions could in principle also account for much softer and broader power-law-like emission spectra. We introduce a 'leading blob' scenario, applicable to active flaring episodes, when one (or a few) of these components become distinct over the 'background' emission, producing hard spectral features and/or hardening of the observed spectra. We show that this model can explain the peculiar high-energy characteristics of Mkn 501 in 2009, with evidence for flaring activity and strong spectral hardening at the highest {gamma}-ray energies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

THE COUPLING BETWEEN THE CORE/CUSP AND MISSING SATELLITE PROBLEMS

We calculate the energy that baryons must inject into cold dark matter (CDM) halos in order to remove centrally divergent DM cusps on scales relevant to observations of dwarf spheroidal galaxies (dSphs). We estimate that the CDM halos often associated with the Milky Way's dSphs (M{sub vir}/M{sub Sun} {approx} 10{sup 9-10}) require {Delta}E {approx} 10{sup 53-55} erg in order to form cores on scales comparable to the luminous size of these galaxies. While supernova Type II (SNeII) explosions can in principle generate this energy, the actual contribution is limited by the low star formation efficiency implied by the abundance of luminous satellites. Considering that CDM's well-known 'core/cusp' and 'missing satellite' problems place opposing demands on star formation efficiencies, existing observational evidences for large cores in the most luminous dSphs require that CDM models invoke some combination of the following: (1) efficient (of the order of unity) coupling of SNeII energy into dark matter particles, (2) star formation histories peaking at unexpectedly high redshifts (z {approx}> 6), (3) a top-heavy stellar initial mass function, and/or (4) substantial satellite disruption or other stochastic effects to ease the substructure abundance constraints. Our models show that the tension between CDM problems on small scales would increase if cored DM profiles were to be found in fainter dwarfs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

PLANET FORMATION IN CIRCUMBINARY CONFIGURATIONS: TURBULENCE INHIBITS PLANETESIMAL ACCRETION

The existence of planets born in environments highly perturbed by a stellar companion represents a major challenge to the paradigm of planet formation. In numerical simulations, the presence of a close binary companion stirs up the relative velocity between planetesimals, which is fundamental in determining the balance between accretion and erosion. However, the recent discovery of circumbinary planets by Kepler establishes that planet formation in binary systems is clearly viable. We perform N-body simulations of planetesimals embedded in a protoplanetary disk, where planetesimal phasing is frustrated by the presence of stochastic torques, modeling the expected perturbations of turbulence driven by the magnetorotational instability. We examine perturbation amplitudes relevant to dead zones in the midplane (conducive to planet formation in single stars), and find that planetesimal accretion can be inhibited even in the outer disk (4-10 AU) far from the central binary, a location previously thought to be a plausible starting point for the formation of circumbinary planets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

FOSSIL EVIDENCE FOR THE TWO-PHASE FORMATION OF ELLIPTICAL GALAXIES

Massive early-type galaxies (ETGs) have undergone dramatic structural evolution over the last 10 Gyr. A companion paper shows that nearby elliptical galaxies with M{sub *} {>=} 1.3 Multiplication-Sign 10{sup 11} M{sub Sun} generically contain three photometric subcomponents: a compact inner component with effective radius R{sub e} {approx}< 1 kpc, an intermediate-scale middle component with R{sub e} Almost-Equal-To 2.5 kpc, and an extended outer envelope with R{sub e} Almost-Equal-To 10 kpc. Here we attempt to relate these substructures with the properties of ETGs observed at higher redshifts. We find that a hypothetical structure formed from combining the inner and middle components of local ellipticals follows a strikingly tight stellar mass-size relation, one that resembles the distribution of ETGs at z Almost-Equal-To 1. Outside of the central kpc, the median stellar mass surface density profiles of this composite structure agree closest with those of massive galaxies that have similar cumulative number density at 1.5 < z < 2.0 within the uncertainty. We propose that the central substructures in nearby ellipticals are the evolutionary descendants of the ''red nuggets'' formed under highly dissipative (''wet'') conditions at high redshifts, as envisioned in the initial stages of the two-phase formation scenario recently advocated for massive galaxies. Subsequent accretion, plausibly through dissipationless (''dry'') minor mergers, builds the outer regions of the galaxy identified as the outer envelope in our decomposition. The large scatter exhibited by this component on the stellar mass-size plane testifies to the stochastic nature of the accretion events.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

PARTICLE ACCELERATION AT THE HELIOSPHERIC TERMINATION SHOCK WITH A STOCHASTIC SHOCK OBLIQUITY APPROACH

Observations by the plasma and magnetic field instruments on board the Voyager 2 spacecraft suggest that the termination shock is weak with a compression ratio of {approx}2. However, this is contrary to the observations of accelerated particle spectra at the termination shock, where standard diffusive shock acceleration theory predicts a compression ratio closer to {approx}2.9. Using our focused transport model, we investigate pickup proton acceleration at a stationary spherical termination shock with a moderately strong compression ratio of 2.8 to include both the subshock and precursor. We show that for the particle energies observed by the Voyager 2 Low Energy Charged Particle (LECP) instrument, pickup protons will have effective length scales of diffusion that are larger than the combined subshock and precursor termination shock structure observed. As a result, the particles will experience a total effective termination shock compression ratio that is larger than values inferred by the plasma and magnetic field instruments for the subshock and similar to the value predicted by diffusive shock acceleration theory. Furthermore, using a stochastically varying magnetic field angle, we are able to qualitatively reproduce the multiple power-law structure observed for the LECP spectra downstream of the termination shock.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

ASSOCIATION OF SUPRATHERMAL PARTICLES WITH COHERENT STRUCTURES AND SHOCKS

Various mechanisms have been proposed to explain observed suprathermal particle populations in the solar wind, including direct acceleration at flares, stochastic acceleration, shock acceleration, and acceleration by random compression or reconnection sites. Using magnetic field and suprathermal particle data from the Advanced Composition Explorer (ACE), we identify coherent structures and interplanetary shocks, and analyze the temporal association of energetic particle fluxes with these coherent structures. Coherent structures having a range of intensities are identified using the magnetic Partial Variance of Increments statistic, essentially a normalized vector increment. A stronger association of energetic particle flux in the 0.047-4.75 MeV range is found with intense magnetic discontinuities than is found with shocks. Nevertheless, the average profile of suprathermals near shocks is quite consistent with standard models of diffusive shock acceleration, while a significant amount of the energetic particles measured and strong discontinuities are found by ACE within six hours of a shock. This evidence supports the view that multiple mechanisms contribute to the acceleration and transport of interplanetary suprathermal particles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

MASSIVE BLACK HOLE PAIRS IN CLUMPY, SELF-GRAVITATING CIRCUMNUCLEAR DISKS: STOCHASTIC ORBITAL DECAY

We study the dynamics of massive black hole pairs in clumpy gaseous circumnuclear disks. We track the orbital decay of the light, secondary black hole M {sub .2} orbiting around the more massive primary at the center of the disk, using N-body/smoothed particle hydrodynamic simulations. We find that the gravitational interaction of M {sub .2} with massive clumps M {sub cl} erratically perturbs the otherwise smooth orbital decay. In close encounters with massive clumps, gravitational slingshots can kick the secondary black hole out of the disk plane. The black hole moving on an inclined orbit then experiences the weaker dynamical friction of the stellar background, resulting in a longer orbital decay timescale. Interactions between clumps can also favor orbital decay when the black hole is captured by a massive clump that is segregating toward the center of the disk. The stochastic behavior of the black hole orbit emerges mainly when the ratio M {sub .2}/M {sub cl} falls below unity, with decay timescales ranging from ∼1 to ∼50 Myr. This suggests that describing the cold clumpy phase of the interstellar medium in self-consistent simulations of galaxy mergers, albeit so far neglected, is important to predict the black hole dynamics in galaxy merger remnants.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A MECHANISM FOR HYSTERESIS IN BLACK HOLE BINARY STATE TRANSITIONS

We suggest that the hysteretic cycle of black hole state transitions arises from two established properties of accretion disks: the increase in turbulent stress in disks threaded by a net magnetic field and the ability of thick (but not thin) disks to advect such a field radially. During quiescence, magnetic field loops are generated by the magnetorotational instability at the interface between the inner hot flow and outer thin disk. Vertical flux is advected into and accumulates stochastically within the inner flow, where it stimulates the turbulence so that α ∼ 1. The transition to a geometrically thin inner disk occurs when L ∼ α{sup 2} L {sub Edd} ∼ L {sub Edd}, and the first ''thin'' disk to form is itself moderately thick, strongly magnetized, and able to advect field inward. These properties favor episodic jet production. As the accretion rate declines magnetic flux escapes, α decreases to α ∼ 0.01-0.1, and a hot inner flow is not re-established until L << L {sub Edd}. We discuss possible observational consequences of our scenario.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

TESTING THE ASTEROSEISMIC MASS SCALE USING METAL-POOR STARS CHARACTERIZED WITH APOGEE AND KEPLER

Fundamental stellar properties, such as mass, radius, and age, can be inferred using asteroseismology. Cool stars with convective envelopes have turbulent motions that can stochastically drive and damp pulsations. The properties of the oscillation frequency power spectrum can be tied to mass and radius through solar-scaled asteroseismic relations. Stellar properties derived using these scaling relations need verification over a range of metallicities. Because the age and mass of halo stars are well-constrained by astrophysical priors, they provide an independent, empirical check on asteroseismic mass estimates in the low-metallicity regime. We identify nine metal-poor red giants (including six stars that are kinematically associated with the halo) from a sample observed by both the Kepler space telescope and the Sloan Digital Sky Survey-III APOGEE spectroscopic survey. We compare masses inferred using asteroseismology to those expected for halo and thick-disk stars. Although our sample is small, standard scaling relations, combined with asteroseismic parameters from the APOKASC Catalog, produce masses that are systematically higher (<ΔM > =0.17 ± 0.05 M {sub ☉}) than astrophysical expectations. The magnitude of the mass discrepancy is reduced by known theoretical corrections to the measured large frequency separation scaling relationship. Using alternative methods for measuring asteroseismic parameters induces systematic shifts at the 0.04 M {sub ☉} level. We also compare published asteroseismic analyses with scaling relationship masses to examine the impact of using the frequency of maximum power as a constraint. Upcoming APOKASC observations will provide a larger sample of ∼100 metal-poor stars, important for detailed asteroseismic characterization of Galactic stellar populations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

MAGNETIC COMPLEXITY AS AN EXPLANATION FOR BIMODAL ROTATION POPULATIONS AMONG YOUNG STARS

Observations of young open clusters have revealed a bimodal distribution of fast and slower rotation rates that has proven difficult to explain with predictive models of spin down that depend on rotation rates alone. The Metastable Dynamo Model proposed recently by Brown, employing a stochastic transition probability from slow to more rapid spin down regimes, appears to be more successful but lacks a physical basis for such duality. Using detailed 3D MHD wind models computed for idealized multipole magnetic fields, we show that surface magnetic field complexity can provide this basis. Both mass and angular momentum losses decline sharply with increasing field complexity. Combined with observation evidence for complex field morphologies in magnetically active stars, our results support a picture in which young, rapid rotators lose angular momentum in an inefficient way because of field complexity. During this slow spin-down phase, magnetic complexity is eroded, precipitating a rapid transition from weak to strong wind coupling.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

THE MOST INTENSIVE GAMMA-RAY FLARE OF QUASAR 3C 279 WITH THE SECOND-ORDER FERMI ACCELERATION

The very short and bright flare of 3C 279 detected with Fermi-Large Area Telescope in 2013 December is tested by a model with stochastic electron acceleration by turbulences. Our time-dependent simulation shows that the very hard spectrum and asymmetric light curve are successfully reproduced by changing only the magnetic field from the value in the steady period. The maximum energy of electrons drastically grows with the decrease of the magnetic field, which yields a hard photon spectrum as observed. Rapid cooling due to the inverse-Compton scattering with the external photons reproduces the decaying feature of the light curve.The inferred energy density of the magnetic field is much less than the electron and photon energy densities. The low magnetic field and short variability timescale are unfavorable for the jet acceleration model from the gradual Poynting flux dissipation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

STOCHASTICITY AND EFFICIENCY IN SIMPLIFIED MODELS OF CORE-COLLAPSE SUPERNOVA EXPLOSIONS

We present an initial report on 160 simulations of a highly simplified model of the post-bounce core-collapse supernova environment in three spatial dimensions (3D). We set different values of a parameter characterizing the impact of nuclear dissociation at the stalled shock in order to regulate the post-shock fluid velocity, thereby determining the relative importance of convection and the stationary accretion shock instability (SASI). While our convection-dominated runs comport with the paradigmatic notion of a “critical neutrino luminosity” for explosion at a given mass accretion rate (albeit with a nontrivial spread in explosion times just above threshold), the outcomes of our SASI-dominated runs are much more stochastic: a sharp threshold critical luminosity is “smeared out” into a rising probability of explosion over a ∼20% range of luminosity. We also find that the SASI-dominated models are able to explode with 3–4 times less efficient neutrino heating, indicating that progenitor properties, and fluid and neutrino microphysics, conducive to the SASI would make the neutrino-driven explosion mechanism more robust.

79 ASTRONOMY AND ASTROPHYSICS↗